Video Transcript
The following figure shows points
A, B, and C. Two light rays from each point are
shown. Where the paths of the reflected
light rays cross, image 1 is formed of point C, image 2 is formed of point B, and
image 3 is formed of point A. If the points A, B, and C are the
tops of objects that all had their bases touching the optical axis of the mirror,
which object will produce the largest image?
Here, we are given a figure of a
concave mirror with the center of curvature, optical axis, and focal point
labeled. We are also given three points A,
B, and C, each with its own pair of light rays extending from it. One ray from each of the points
travels along a horizontal line, parallel to the optical axis, which means the
reflected rays from them will pass through the focal point. From the question, we know that
each point also corresponds to one of the three images shown in the figure. Point A corresponds to image 3,
point B corresponds to image 2, and point C corresponds to image 1.
We are asked to look at these
images and figure out which image will be the largest if the three points represent
the tops of three objects that are all the same height and rest on the optical
axis. Let’s first recall some information
about concave mirrors and how they form images. Remember that a concave mirror is a
curved mirror whose reflective side is on the inside of the curve facing the center
of curvature. We should consider that concave
mirrors can create both real and virtual images.
Virtual images are formed behind
the mirror and real images are formed in front of the mirror. We can see all three images in
front of the mirror, so we know they are real and can just focus on those types of
images. The real images that concave
mirrors produce are going to be inverted, flipped upside down. And they can be smaller, larger, or
the same size as the object, based on how far away they are from the mirror.
If an object is located further
away than the center of curvature of a concave mirror, its real image will appear
smaller than the object. If it is at the center of curvature
of a concave mirror, its real image will appear to be the same size as the
object. And if an object is located in
front of the center of curvature and behind the focal point of a concave mirror, the
image will appear larger than the object and will be larger the closer to the focal
point the object is.
Now that we know how an image’s
size will change based on the object’s location, let’s take a closer look at our
objects and see what we can figure out about the images they produce. The object with its top at point A
is farther away than the center of curvature, so its corresponding image will appear
to be smaller than the object. The object at point B is in between
the center of curvature and the focal point, so its image will appear larger than
the object. And the object at point C is also
in between the center of curvature and the focal point, so its image will also be
larger than the object.
We have two objects that will have
images larger than them, but remember that images get larger as objects get closer
to the focal point as well. We can see that point C is closer
to the focal point than point B, so the object at point C will produce the largest
image which we can see here. So, the object with its top at
point C is the correct answer.
